Theorem 2.3 (Feldman–Moore [1]})   Let \(E\)  be a
countable Borel equivalence relation on a standard Borel space \((X,\mathcal {B})\) .
Then there is a countable group \(\Gamma \)  of Borel automorphisms of
\((X,\mathcal {B})\)  such that \(E = E_X(\Gamma )\) .

